Gaussian fields and percolation
Dmitry Beliaev
TL;DR
This survey reviews recent advances in understanding the large-scale geometry of smooth Gaussian fields, focusing on level and excursion sets and their potential links to percolation theory.
Contribution
It consolidates research on the large-scale behavior of Gaussian fields and explores their conjectured connection to percolation, highlighting recent progress and open questions.
Findings
Progress in understanding the geometry of Gaussian fields
Conjectured connections between Gaussian fields and percolation theory
Open problems in large-scale behavior analysis
Abstract
In the last two decades there was a lot of progress in understanding the geometry of smooth Gaussian fields. This survey aims to cover one particular line of research: the large scale behaviour of level and excursion sets and their (conjectured) connection to the percolation theory.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Mathematical Dynamics and Fractals · Geometry and complex manifolds